1. A stock price is currently $100. The price volatility of this stock is = 0.20, and the risk-free interest rate is 3% per annum with monthly compounding.
   1. What is the replicating portfolio and price of a two-month European put option with a strike price of $102?
   2. What is the replicating portfolio and price of a two-month European call option with a strike price of $102?
   3. Verify that put-call parity is satisfied with these prices.

2. For the stock and risk free rate in problem 1, consider four-month options to be priced with a two-step binomial lattice.
   1. What is the risk-neutral probability for this stock over a two month period?
   2. Confirm that your answer is correct by repricing the put in 1.a. using risk-neutral valuation.
   3. Price a four-month European put option on this stock with a strike price of 102, using risk-neutral valuation.
   4. Price a four-month American put option on this stock with a strike price of 102, using risk-neutral valuation.

3. What is the initial replicating portfolio for the American put option in 2.d.? Confirm that the price of this portfolio agrees with your price in 2.d. Hint: You know the two values of this put option at time t=2/12.